Look for a GCF first, then factor the remaining trinomial

Question

12x^2+2x-2

1. What is the greatest common factor?
2. write your answer in factored form:

32w^2-16w+2

1. what is the greatest common factor?
2. write your answer in factored form:

Answer 1

Well for the first.

1. The highest integer that will divide each term is 2
2. No power of x will divide each term

So the greatest common factor is 2

12x² + 2x - 2 = 2 (6x² + x - 1)

The parenthesis factorises as (3x-1) (2x+1) so the final factorisation is 6 (3x-1) (2x+1)

Again for the second greatest common factor is 2.

2 (16w² - 8w + 1)

Parenthesis factors to (4w-1) (4w-1) = (4w-1)², so final result is 2 (4w-1)²